Is there a way to talk to an employee about his stutter for professional development/promotion?

Is there a way to talk to an employee about his stutter for professional development/promotion? I have a part time employee with a mild stutter. He's been with us a year, he's a great worker, and I really want to get him into a fulltime role. But the only fulltime position I have is outreach, which involves a lot of public speaking, engagement, relationship building, i.e. a lot of talking. I've thought about suggesting he get involved in Toastmasters or something similar to build experience and confidence in public speaking so we can get him into an outreach role. But is that crossing a line? I know he wants a fulltime position badly, and he's expressed interest in doing outreach. So is there a way to discuss his stutter professionally, or is it off limits, like discussing health issues? And if it is something I can discuss with him, any suggestions on how I should go about it?